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| author | Matthias Vogelgesang <matthias.vogelgesang@kit.edu> | 2017-11-12 09:48:27 -0800 |
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| committer | Matthias Vogelgesang <matthias.vogelgesang@kit.edu> | 2017-11-12 10:45:40 -0800 |
| commit | 92de2c687d36db08730dad26f614341604d3cfab (patch) | |
| tree | 21a633afcd0c2904132f540b01b76733577901fa /docs | |
| parent | 36244b7fbee64bfd083f9ebcebdf7ad9d3427767 (diff) | |
| download | ufo-filters-92de2c687d36db08730dad26f614341604d3cfab.tar.gz ufo-filters-92de2c687d36db08730dad26f614341604d3cfab.tar.bz2 ufo-filters-92de2c687d36db08730dad26f614341604d3cfab.tar.xz ufo-filters-92de2c687d36db08730dad26f614341604d3cfab.zip | |
Add examples for reconstruction
Diffstat (limited to 'docs')
| -rw-r--r-- | docs/examples.rst | 47 | ||||
| -rw-r--r-- | docs/index.rst | 9 |
2 files changed, 56 insertions, 0 deletions
diff --git a/docs/examples.rst b/docs/examples.rst new file mode 100644 index 0000000..cc7c44d --- /dev/null +++ b/docs/examples.rst @@ -0,0 +1,47 @@ +=================== +Computed Tomography +=================== + +Reconstruction +============== + +Filtered backprojection +----------------------- + +To reconstruct from sinograms using the analytical filtered backproject method +[KaSl01]_, you have to feed the sinograms into :gobj:class:`fft` → +:gobj:class:`filter` → :gobj:class:`ifft` → :gobj:class:`backproject` to obtain +slices one by one:: + + ufo-launch \ + dummy-data width=$DETECTOR_WIDTH height=$N_PROJECTIONS number=$N_SLICES ! \ + fft dimensions=1 ! \ + filter ! \ + ifft dimensions=! ! \ + backproject axis-pos=$AXIS ! \ + null + + +Direct Fourier inversion +------------------------ + +In this example we use the Fourier slice theorem to obtain slices directly from +projection data [KaSl01]_ and use a sinc kernel to interpolate in the Fourier +space. To reconstruct, you have to feed the sinograms into :gobj:class:`zeropad` +→ :gobj:class:`fft` → :gobj:class:`dfi-sinc` → :gobj:class:`swap-quadrants` → +:gobj:class:`ifft` → :gobj:class:`swap-quadrants`:: + + ufo-launch \ + dummy-data width=$DETECTOR_WIDTH height=$N_PROJECTIONS number=$N_SLICES ! \ + zeropad center-of-rotation=$AXIS ! \ + fft dimensions=1 auto-zeropadding=0 ! \ + dfi-sinc ! \ + swap-quadrants ! \ + ifft dimensions=2 ! \ + swap-quadrants ! \ + null + + +.. rubric:: References + +.. [KaSl01] Kak, A. C., & Slaney, M. (2001). Principles of Computerized Tomographic Imaging (Philadelphia, PA: SIAM). diff --git a/docs/index.rst b/docs/index.rst index d162e7b..7e3883e 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -25,6 +25,15 @@ Reference contrib/index +Examples +======== + +.. toctree:: + :maxdepth: 2 + + examples + + Additional notes ================ |